Related papers: On \omega-categorical simple theories

For a finite group $G$, let $\sigma(G)$ be the number of subgroups of $G$ and $\sigma_\iota(G)$ the number of isomorphism types of subgroups of $G$. Let $L=L_r(p^e)$ denote a simple group of Lie type, rank $r$, over a field of order $p^e$…

Let $X$ be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by $F$ a smooth model of a generic irreducible component in fibers of the canonical…

A recent article of Chernikov, Hrushovski, Kruckman, Krupinski, Moconja, Pillay and Ramsey finds the first examples of simple structures with formulas which do not fork over $\emptyset$ but are universally measure zero. In this article we…

Let T be a countable, small simple theory. In this paper, we prove for such T, the notion of Lascar Strong type coincides with the notion of a strong type,over an arbitrary set.

We prove that each \omega-categorical, generically stable group is solvable-by-finite.

We prove that every \omega-categorical, generically stable group is nilpotent-by-finite and that every \omega-categorical, generically stable ring is nilpotent-by-finite.

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

In this short note, we will show the following weak evidence of S. Lang conjecture over function fields. Let f : X ---> Y be a projective and surjective morphism of algebraic varieties over an algebraically closed field k of characteristic…

We study possibilities for almost $n$-ary and $n$-aritizable theories. Their dynamics both in general case, for $\omega$-categorical theories, and with respect to operations for theories are described.

We give a new description of computads for weak globular $\omega$-categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads, and allows a new definition of $\omega$-category that…

We prove that suitably generic pairs of linear equations on an even number of variables are uncommon. This verifies a conjecture of Kam\v{c}ev, Morrison and the second author. Moreover, we prove that any large system containing such a…

In the paper we introduce a weak set theory $\mathsf{H}_{<\omega}$ . A formalization of arithmetic on finite von Neumann ordinals gives an embedding of arithmetical language into this theory. We show that $\mathsf{H}_{<\omega}$ proves a…

It is conjectured by de Jong that, if $X$ is a connected projective smooth variety over an algebraically closed field $k$ of characteristic $p>0$ with trivial etale fundamental group, any convergent isocrystal $\mathcal{E}$ on $X$ is…

We give a potential alternative definition of a weak infinite dimensional category, in an unbiased fashion, using one one dimensional quiver with composition and extra structure.

We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and…

We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…

A countable group is C*-simple if its reduced C*-algebra is simple. It is well known that C*-simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit…

We show that a natural, two sorted $\cL_{\omega_1,\omega}$ theory involving the modular $j$-function is categorical in all uncountable cardinaities. It is also shown that a slight weakening of the adelic Mumford-Tate conjecture for products…

Uniform metastable convergence is a weak form of uniform convergence for a family of sequences. In this paper we explore the way that metastable convergence stratifies into a family of notions indexed by countable ordinals. We give two…

We extend a dichotomy between 1-basedness and supersimplicity proved in a previous paper. The generalization we get is to arbitrary language, with no restrictions on the topology (we do not demand type-definabilty of the open set in the…